论文标题
第二学位和任意维度的全体形态叶子
Holomorphic foliations of degree two and arbitrary dimension
论文作者
论文摘要
令$ \ mathcal {f} $为$ \ mathbb {p}^n $的$ 2 $ $ 2 $的全体形状叶面，带有dimension $ k \ geq 2 $。我们证明，$ \ Mathcal {f} $是代数的，或$ \ Mathcal {f} $是curves a curviation of $ \ mathbb {p}^{p}^{n-k+1} $的线性撤回，或+1}，2）$或$ \ MATHCAL {f} $是类型$（1^{n-k+3}）$的对数叶子，或$ \ Mathcal {f} $是$ \ Mathbb {p} lielge 2 on dimension-dimension-dimension-dimension-dimension-dimension-lie-2 liel-2 foliation的线性下拉，lielge alla $ \ mathfrak {aff}（\ mathbb {c}）$。作为副产品，我们在$ \ mathbb {p}^n $上描述了泊松结构的几何形状，并以二级等级为二。
Let $\mathcal{F}$ be a holomorphic foliation of degree $2$ on $\mathbb{P}^n$ with dimension $k\geq 2$. We prove that either $\mathcal{F}$ is algebraically integrable, or $\mathcal{F}$ is the linear pull-back of a degree-2 foliation by curves on $\mathbb{P}^{n-k+1}$, or $\mathcal{F}$ is a logarithmic foliation of type $(1^{n-k +1},2)$, or $\mathcal{F}$ is a logarithmic foliation of type $(1^{n-k+3})$, or $\mathcal{F}$ is the linear pull-back of a degree-2 foliation of dimension 2 on $\mathbb{P}^{n-k+2}$ tangent to an action of the Lie algebra $\mathfrak{aff}(\mathbb{C})$. As a byproduct, we describe the geometry of Poisson structures on $\mathbb{P}^n$ with generic rank two.
